Consider the following insertion sort algorithm to sort a given array of n numbers. The first and second numbers are compared; if they are out of order, they are swapped so that they are in sorted order. Then the third number is compared with the second; if it is not in the proper order, it is swapped with the second and then compared with the first. Iteratively, the Kth number is handled by swapping it downward until the first k numbers are in sorted order. Determine the expected (i.e., average) number of swaps that need to be made with insertion sort when the input is a random permutation of n distinct numbers, i.e., the input is equally likely to be any of the n! permutations